Final answer:
The x-coordinates of the points where the graphs of y = 4^-x and y = 2^-x+1 intersect can be found by solving the equation 4^-x = 2^-x+1. The solution to 4^x = 2^x+1 can be found by creating tables and comparing the y-values. The equation 4^x - 2^x+1 can be solved graphically by plotting the graphs of y = 4^x and y = 2^x+1.
Step-by-step explanation:
Part A: The x-coordinates of the points where the graphs of the equations y = 4^-x and y = 2^-x+1 intersect are the solutions of the equation 4^-x = 2^-x+1. To find these solutions, we can rewrite the equation as (2^2)^-x = (2^1)^-x+1. Using the property (a^m)^n = a^(m*n), we can simplify the equation to 2^-2x = 2^-x+1. Since the bases are the same, we can equate the exponents and solve for x. -2x = -x+1. Adding x to both sides gives us -x = 1. Multiplying both sides by -1 gives us x = -1, which is the solution to the equation 4^-x = 2^-x+1.
Part B: To find the solution to 4^x = 2^x+1, we can create tables by plugging in integer values of x between -2 and 2 into both equations. Evaluating the equations for these values of x will give us the corresponding y-values. We can then compare the y-values to find the points where the graphs intersect.
Part C: To solve the equation 4^x - 2^x+1 graphically, we can plot the graphs of y = 4^x and y = 2^x+1 on a coordinate plane. The x-coordinates of the points of intersection will be the solutions to the equation. We can use a graphing calculator or computer software to plot the graphs and find the intersection points.